Rewrite 18y x 4x using Commutative Property

What does the range and mean tell you about data?

Nady [450]

The approximate middle value

4 0

2 years ago

Read 2 more answers

Verify that P = Ce^t /1 + Ce^t is a one-parameter family of solutions to the differential equation dP dt = P(1 − P).

NemiM [27]

Answer:

See verification below

Step-by-step explanation:

We can differentiate P(t) respect to t with usual rules (quotient, exponential, and sum) and rearrange the result. First, note that

$1-P=1-\frac{ce^t}{1+ce^t}=\frac{1+ce^t-ce^t}{1+ce^t}=\frac{1}{1+ce^t}$

Now, differentiate to obtain

$\frac{dP}{dt}=(\frac{ce^t}{1+ce^t})'=\frac{(ce^t)'(1+ce^t)-(ce^t)(1+ce^t)'}{(1+ce^t)^2}$

$=\frac{(ce^t)(1+ce^t)-(ce^t)(ce^t)}{(1+ce^t)^2}=\frac{ce^t+ce^{2t}-ce^{2t}}{(1+ce^t)^2}=\frac{ce^t}{(1+ce^t)^2}$

To obtain the required form, extract a factor in both the numerator and denominator:

$\frac{dP}{dt}=\frac{ce^t}{1+ce^t}\frac{1}{1+ce^t}=P(1-P)$

3 0

3 years ago

How can 8 students share a pizza cut into 12 slices without cutting any of the slices?

Triss [41]

Hmmm...
We have to divide 12 by 8, since we need to see how 8 students will share 12 slices.

12/8=1 and 1/2

So, each student can have a slice and a half, but since we aren't allowed to cut the slices...

We can let each student have one slice, with 4 left over, so...

Every student can have one slice, and then half can have a second slice :)!

I'm not sure if that is what was meant by the question, but that was all I could think of.

I hope I helped! :)

3 0

3 years ago

An animal shelter spends 5.50 per day to care for each bird and 8.50 per Day to care for each cat and a notice that the shelter

Deffense [45]

Answer:

19 birds

Step-by-step explanation:

First, I wrote my two equations:

5.5x +8.5y = 291.5

x + y = 41

Next, I got the variable y by itself in the second equation. Subtract x to get y = -x + 41. Then, I substituted what y equaled into the first equation. It should look like this: 5.5x + 8.5(-x+41) = 291.5. Distribute 8.5 to get 5.5x -8.5x + 348.5 = 291.5. Subtract 5.5x and 8.5x to get -3x. It should look like this: -3x + 348.5= 291.5. Subtract 348.5 from 291.5 to get -57. Now, you should have -3x = -57. Divide -3 from both sides, to get x = 19. So, there are 19 birds. If you want to go even further, 41-19= 22, which means there are 22 cats. Hope this helped!

6 0

3 years ago

the length of a rectangular building is 6 feet less than 3 times t he width. The perimeter is 120 feet. Find the width and the l

garri49 [273]

Call the width x. Note that the length is 3x-6. We know that double the width plus double the length is 120, so we write an equation:

$2(x)+2(3x-6)=120$
$2x+6x-12=120$
$8x-12=120$
$8x=132$
$x=16.5$
If x is 16.5, the width is 16.5, and the length is $3 \cdot 16.5 - 6 = 43.5$ .

5 0

3 years ago